The Garman Kohlhagen Model
The Garman Kohlhagen model is suitable for evaluating European style options on spot foreign exchange. This model alleviates the restrictive assumption used in the Black Scholes model that borrowing and lending is performed at the same risk free rate. In the foreign exchange market there is no reason that the risk free rate should be identical in each country. Any interest rate differential between the two currencies will impact the value of the FX option. The risk free foreign interest rate in this case can be thought of as a continuous dividend yield being paid on the foreign currency. Since an option holder does not receive any cash flows paid from the underlying instrument, this should be reflected in a lower option price in the case of a call or a higher price in the case of a put. The Garman Kohlhagen model provides a solution by subtracting the present value of the continuous cash flow from the price of the underlying instrument.
Assumptions under which the formula was derived include:
- the option can only be exercised on the expiry date (European style);
- there are no taxes, margins or transaction costs;
- the risk free interest rates (domestic and foreign) are constant;
- the price volatility of the underlying instrument is constant; and
- the price movements of the underlying instrument follow a lognormal distribution.
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